Question

Find the area of shaded region​

Answer 1

Answer:

168.444m^2

Step-by-step explanation:

Use the formula of Heron's.

area of triangle having sides of different length :

√s(s-a)(s-b)(s-c)

Where a, b ,and c are the sides

s = half perimeter = (a+b+c)/2

for smaller triangle:-

here from figure,

let,a= 3 , b = 4, c =5

s = half perimeter = (a+b+c)/2 = (3+4+5)/2 = 6

so, Area = √s(s-a)(s-b)(s-c)

= √[6*(6-3)*(6-4)*(6-5)]

= √[6*6*2*1]

= √72  = 6√2 m^2

= 8.485m^2   [ √2 = 1.414]

for larger triangle:-

here from figure,

let,a= 15 , b = 30, c =41

s = half perimeter = (a+b+c)/2 = (15+30+41)/2 = 43

so, Area = √s(s-a)(s-b)(s-c)

= √[43*(43-15)*(43-30)*(43-41)]

= √[43*28*13*2]

= √31304

= 176.929 m^2

so, area of shaded area = area of larger triangle - area of smaller triangle

= 176.929 m^2 - 8.485m^2

= 168.444m^2